In this first part the general aspects of accepted or recommended parameter definitions useful to evaluate quasi-periodic signals frequency stability are introduced, based on the most common model suitable for discussion and development. The parameters belong to two different areas: the time and the frequency domains, with different experimental techniques and theoretical approaches. The two domains, however, are linked to each other and they support each other in picking up experimental data to be fruitfully applied in science and technology. This paper is mainly concerned with the developments in experimental methods and with the Allan variance and the Modified Allan variance analyses.